Regular Seminar Julian Sonner (University of Geneva)
The recent focus on entanglement entropy in holography has many motivations, ranging from the applied (e.g. AdS/CMT) to the foundational (emergence of gravity). For all of these programs It is important to find examples, where the quantities of interest can be directly calculated in strongly-coupled field theories and, moreover, the dual geometry constructed at strong coupling. In this talk I will describe joint work with Crossley and Dyer on using localization methods to obtain entanglement and (super-) Renyi entropies of the N=4 SYM theory with gauge group SU(N) in 4D at all values of the ít Hooft coupling \lambda and number of colors N. Since obtaining quantities like entanglement and Renyi entropies involves working on singular spaces, which typically break the supersymmetry, we focus on a supersymmetric generalization, the so-called super-Renyi entropy where the supersymmetry breaking effects of the singularities are suitably compensated. I will also discuss dual gravity solutions as five-dimensional BPS black holes with hyperbolic horizon. I will conclude with a description of Wilson loops, that is the contribution to the entanglement and Renyi entropies due to adding fundamental matter to the theory.